Asymptotic behaviour of CastelnuovoMumford regularity
Author:
Vijay Kodiyalam
Journal:
Proc. Amer. Math. Soc. 128 (2000), 407411
MSC (1991):
Primary 13D02; Secondary 13D40
Published electronically:
July 6, 1999
MathSciNet review:
1621961
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Abstract: Let be a polynomial ring over a field. For a graded module generated in degree at most , the CastelnuovoMumford regularity of each of (i) its symmetric power, (ii) its torsionfree symmetric power and (iii) the integral closure of its torsionfree symmetric power is bounded above by a linear function in with leading coefficient at most . For a graded ideal of , the regularity of is given by a linear function of for all sufficiently large . The leading coefficient of this function is identified.
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 Aaron Bertram, Lawrence Ein, Robert Lazarsfeld, Vanishing theorems, a theorem of Severi, and the equations defining projective varieties, Journal of the American Mathematical Society 4 (1991), 587602. MR 92g:14014
 [Brt]
 Aaron Bertram, An application of a log version of the Kodaira vanishing theorem to embedded projective varieties, Preprint alggeom/9707001.
 [Chn]
 Karen A. Chandler, Regularity of the powers of an ideal, Communications in Algebra 25 (12) (1997), 37733776. CMP 98:04
 [Cnc]
 Aldo Conca, Hilbert function and resolutions of the powers of the ideal of the rational normal curve, Preprint.
 [CncHrzTrnVll]
 Aldo Conca, Jurgen Herzog, Ngo Viet Trung, Giuseppe Valla, Diagonal subalgebras of bigraded algebras and embeddings of blowups of projective spaces, American Journal of Mathematics 119 (4) (1997), 859902. CMP 97:17
 [CtkHrzTrn]
 Dale Cutkosky, Jurgen Herzog, Ngo Viet Trung, Asymptotic behaviour of the CatelnuovoMumford regularity, Preprint.
 [Snb]
 David Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, SpringerVerlag, 1995. MR 97a:13001
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 David Eisenbud, Shiro Goto, Linear free resolutions and minimal multiplicity, Journal of Algebra 88 (1984), 89133. MR 85f:13023
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 A. V. Geramita, A. Gimigliano, Y. Pitteloud, Graded Betti numbers of some embedded rational nfolds, Mathematische Annalen 301 (1995), 363380. MR 96f:13022
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 Le Tuan Hoa, Ngo Viet Trung, On the CastelnuovoMumford regularity and the arithmetic degree of monomial ideals, Mathematische Zeitschrift, To appear.
 [Res]
 D. Rees, Reduction of modules, Mathematical Proceedings of the Cambridge Philosophical Society 101 (1987), 431448. MR 88a:13001
 [SmtSwn]
 Karen E. Smith, Irena Swanson, Linear bounds on growth of associated primes, Communications in Algebra, 25 (1997), 30713079. CMP 97:17
 [Str]
 Bernd Sturmfels, Four counterexamples in combinatorial algebraic geometry, Preprint.
 [Swn]
 Irena Swanson, Powers of ideals: Primary decompositions, ArtinRees lemma and regularity, Mathematische Annalen 307 (1997), 299313. MR 97j:13005
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Additional Information
Vijay Kodiyalam
Affiliation:
The Institute of Mathematical Sciences, Chennai, India 600113
Email:
vijay@imsc.ernet.in
DOI:
http://dx.doi.org/10.1090/S0002993999050200
PII:
S 00029939(99)050200
Received by editor(s):
October 28, 1997
Received by editor(s) in revised form:
April 15, 1998
Published electronically:
July 6, 1999
Communicated by:
Wolmer V. Vasconcelos
Article copyright:
© Copyright 1999 American Mathematical Society
